How do you factor #5x^4 + x^3 - 22x^2 - 4x + 8#?
The result is
The procedure is the following:
You have to apply Ruffini's Rule trying the divisors of the independent term (in this case, the divisors of 8) until you find one that makes the rest of the division zero.
I started with +1 and -1 but it did not work, but if you try (-2) you get it:
! 5 1 -22 -4 8 -2! -10 +18 +8 -8 _____________________ 5 -9 -4 +4 0
What you have here is that
Now you have got one factor (x+2) and you have to keep going the same process with
If you try now with +2 you will get it:
! 5 -9 -4 4 2 ! 10 2 -4 __________________ 5 +1 -2 0
So, what you have now is that
And summing up what we have done until now:
Now, you have got two factors: (x+2) and (x-2) and you have to decompose
In this case, instead of applying Ruffini's Rule, we shall apply the classic resolution formula to the quadratic equation:
So what we have now is that
So the solution is: